Questions asked by Abdel M.

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• Can a titration be applied to determine the concentration Na3PO4(aq) and NaH2PO4(aq) in a solution mixture of the two salts using HCl and phenolphthalein and methyl orange indicators?
  
• Why carboxylic acids act neither like aldehydes nor like ketones based on resonance?
  
• Show that it is possible to find graphs with equations of the forms y=A-(x-a)^2 and y=B+(x-b)^2 with A>B which do not intersect?
  
• Why is it that the tangent lines to the hyperbola y=1/x at any arbitrary point (x0,y0) intersect the x-axis at (2x0,0) and the y-axis at (0,2y0)?
  
• How do we know when a linear approximation is truly depicting a good approximation of the curve of a nonlinear function near some base point?
  
• Prove that if f(x) is increasing and it has a derivative at a, then f'(a) >= 0. (You may use the fact that a positive function has a limit > 0.)?
  
• a) An airline will fill 100 seats of its aircraft at a fare of $200. For every $5 increase in the fare, the plane loses two passengers. For every decrease of $5, the company gains two passengers. What price maximizes revenue?
  
• Related rates-Weight on rope word problem?
  
• What could go wrong with Newtons Method?
  
• Derivation of the equation of a Hypocycloid?
  
• Definition of the definite integrals?
  
• Proof of the fundamental theorem of calculus?
  
• Find the volume of the region in 3-space with x > 0, y > 0 and z > 0 given by z^2/2 < x + y < z? Hint: First find the area of the horizontal cross-sections
  
• Find the average height of a point on a unit semi-circle?
  
• The intuition behind L'hopital's rule and the conditions which make it applicable?
  
• Convergence and divergence of sequences?
  
• Error estimate of Alternating Series (Proof)?
  
• What is the horizontal range of the stone when the stone strikes the ground?